Lec 1 | MIT 18.06 Linear Algebra, Spring 2005
2. Elimination with Matrices.
3. Multiplication and Inverse Matrices
Lec 4 | MIT 18.06 Linear Algebra, Spring 2005
5. Transposes, Permutations, Spaces R^n
6. Column Space and Nullspace
7. Solving Ax = 0: Pivot Variables, Special Solutions
8. Solving Ax = b: Row Reduced Form R
9. Independence, Basis, and Dimension
10. The Four Fundamental Subspaces
11. Matrix Spaces; Rank 1; Small World Graphs
12. Graphs, Networks, Incidence Matrices
13. Quiz 1 Review
14. Orthogonal Vectors and Subspaces
15. Projections onto Subspaces
16. Projection Matrices and Least Squares
Lec 17 | MIT 18.06 Linear Algebra, Spring 2005
18. Properties of Determinants
19. Determinant Formulas and Cofactors
20. Cramer's Rule, Inverse Matrix, and Volume
Lec 21 | MIT 18.06 Linear Algebra, Spring 2005
22. Diagonalization and Powers of A
23. Differential Equations and exp(At)
Lec 24 | MIT 18.06 Linear Algebra, Spring 2005
Lec 24b | MIT 18.06 Linear Algebra, Spring 2005
Lec 25 | MIT 18.06 Linear Algebra, Spring 2005
26. Complex Matrices; Fast Fourier Transform
27. Positive Definite Matrices and Minima
Lec 28 | MIT 18.06 Linear Algebra, Spring 2005
Lec 29 | MIT 18.06 Linear Algebra, Spring 2005
30. Linear Transformations and Their Matrices
Lec 31 | MIT 18.06 Linear Algebra, Spring 2005
32. Quiz 3 Review
33. Left and Right Inverses; Pseudoinverse
34. Final Course Review
This series of videos covers the fundamentals of linear algebra, including solving systems of linear equations, linear combinations, and multiplying matrices by vectors. It also explains how to draw pictures to represent the algebra and geometry of linear combinations, how to solve three-dimensional linear equations, and how to think of matrix multiplication as a linear combination of the columns of the matrix. Finally, it discusses the concept of nine vectors in nine dimensional space and how it relates to linear algebra.
